Factoriser les expressions suivantes :
F = (2x + 1)² + (2x + 1)(x + 3)
= (2x + 1)(2x + 1) + (2x + 1)(x + 3) = (2x + 1) [(2x + 1) + (x + 3)]
= (2x + 1)(3x + 4)
G = (5x – 2)(2x + 7) – (5x – 2) = (5x – 2)(2x + 7) – 1(5x – 2) = (5x – 2) [(2x + 7) – 1]
= (5x – 2)(2x + 6) = 2(5x – 2)(x + 3)
H = 7x – 49 + 14x² = 7(x – 7 + 2x²)
I = 9x² + 12x + 4
= (3x)² + 2 × 3x × 2 + 2² = (3x + 2)²
J = (2x – 7)(x + 4) – (2x – 7)(4x + 1) = (2x – 7) [(x + 4) – (4x + 1)]
= (2x – 7)(– 3x + 3) = 3(2x – 7)(– x + 1)
K = (4x – 1)² + (2x – 5)(4x – 1) = (4x – 1) [(4x – 1) + (2x – 5)]
= (4x – 1)(6x – 6) = 6(4x – 1)(x – 1)
L = (x + 7)(3x – 1) + 7x + 49 = (x + 7)(3x – 1) + 7(x + 7) = (x + 7) [(3x – 1) + 7]
= (x + 7)(3x + 6) = 3(x + 7)(x + 2)
M = 16x² – 81 = (4x)² – 9² = (4x – 9)(4x + 9)
N = 49x² – 1 4 = (7x)² –
1 2
² =
7x – 1
2
7x + 1
2 O = 9x² + 30x + 25
= (3x)² + 2 × 3x × 5 + 5² = (3x + 5)²
P = (2x + 3)² – 49 = (2x + 3)² – 7²
= [(2x + 3) – 7] [(2x + 3) + 7]
= (2x – 4)(2x + 10) = 2(x – 2) × 2(x + 5) = 4(x – 2)(x + 5)
